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The number of passengers on a certain bus to Houston at any given time
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04 Mar 2025, 00:52
04 Mar 2025, 00:52
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The number of passengers on a certain bus to Houston at any given time is given by the equation $\(P=-2(S-4)^2+32\)$, where $P$ is the number of passengers and $S$ is the number of stops that the bus has made since the beginning of its route. If the bus begins its route without any passenger, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?
(A) 32
(B) 30
(C) 24
(D) 14
(E) 0
(A) 32
(B) 30
(C) 24
(D) 14
(E) 0
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The number of passengers on a certain bus to Houston at any given time
[#permalink]
04 Mar 2025, 02:46
04 Mar 2025, 02:46
if you observe carefully , you'll realise that at S = 4, P has Max value which is 32 since no matter what value you choose for S it will always be subtracted from 32 except at S = 4 then, P = 0 -32 = 32
from the question we are asked to find the value of P 2 stops after the stop have Max P so we need to find the value of P at S = 4+2
so
P = -2(6-4)^2 + 32 = 24
option C is correct
i have a shortcut for these types of questions
if you ever come across an equation which requires you to find the Max or Min value of it
differentiate it
like this
DP/DS = -2*2(S-4)(-4) and equate it to 0 (its a concept of finding max or min of a function using differentiation, its quite easy, look it up on youtube)
and you'll get S = 4
which means at S = 4 P has max value
lemme know if this solution is helpful by kudos
from the question we are asked to find the value of P 2 stops after the stop have Max P so we need to find the value of P at S = 4+2
so
P = -2(6-4)^2 + 32 = 24
option C is correct
i have a shortcut for these types of questions
if you ever come across an equation which requires you to find the Max or Min value of it
differentiate it
like this
DP/DS = -2*2(S-4)(-4) and equate it to 0 (its a concept of finding max or min of a function using differentiation, its quite easy, look it up on youtube)
and you'll get S = 4
which means at S = 4 P has max value
lemme know if this solution is helpful by kudos
gmatclubot
The number of passengers on a certain bus to Houston at any given time [#permalink]
04 Mar 2025, 02:46
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